The transistor on$-$state characteristic is shown below.

$($i$)$ An engineer wants to use the common source circuit to make an amplifier. If they assume $V_{DD}=8V$ and a maximum signal voltage of $1$ V $,$ what would be a suitable quiescent operating point for the circuit? Explain your choice clearly.

$(5$ marks$)$

$($ii$)$ Calculate the value of the transconductance $($gm$)$ of the BS$170$ transistor at $25$ C and $Vgs=5V$

$(3$ marks$)$

The circuit of a common source MOSFET amplifier is shown below.

$(5$ marks$)$

$($iv$)$ What advantage does this circuit have over the common emitter circuit in terms of selecting component values for the bias resistors to reduce power consumption?

$(4$ marks$)$

$($v$)$ If the gain of the common source circuit is:

$A_{?}$

$u0=-\frac{g_m{R}_D}{1+g_m{R}_S}$

Propose values of $R_D$ and $R_s$ to give a gain of $100$

$(4$ marks$)$

$($vi$)$ What is the function of the $C_{in}$ and $C_{\text{o}\text{u}\text{t}}$ capacitors?